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ON SUBSONIC AND SUBSONIC-SONIC FLOWS IN THE INFINITY LONG NOZZLE WITH GENERAL CONSERVATIVES FORCE

Acta Mathematica Scientia 2017年第3期37卷 752-767页

作者：顾旭旻王天怡 Department of Mathematics Shanghai University of Finance and Economics Shanghai 200433 China Department of Mathematics School of Science Wuhan University of Technology Wuhan 430070 China Gran Sasso Science Institute viale Francesco Crispi 7 67100 L 'Aquila Italy

In this article, we study irrotational subsonic and subsonic-sonic flows with gen- eral conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.

关键词： Steady flow homentropic irrotation subsonic flow subsonic-sonic limit

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On Subsonic and Subsonic-Sonic Flows with General Conservatives Force in Exterior Domains

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Acta Mathematicae Applicatae Sinica 2023年第1期39卷 3-16页

作者： Xumin GU Tian-Yi WANG Department of Mathematics Shanghai University of Finance and EconomicsShanghai 200433China Department of Mathematics School of ScienceWuhan University of TechnologyWuhan 430070China The Institute of Mathematical Sciences the Chinese University of Hong KongShatinN.T.Hong Kong Gran Sasso Science Institute viale Francesco Crispi767100 L'AquilaItaly

In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic case, we introduce a modified cut-off system depending on the conservative forces which needs the varied Bers skill, and construct the solution by the new variational formula. Moreover, comparing with previous results, our result extends the pressure-density relation to the general case. Afterwards we obtain the subsonic-sonic limit solution by taking the extract subsonic solutions as the approximate sequences.

关键词： steady fow homentropic irrotation subsonic fow subsonic-sonic limit

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Numerical Solution of Parabolic in Partial Differential Equations (PDEs) in One and Two Space Variable

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Journal of Applied Mathematics and Physics 2022年第2期10卷 311-321页

作者： Mariam Almahdi Mohammed Mu’lla Amal Mohammed Ahmed Gaweash Hayat Yousuf Ismail Bakur Department of Mathematics University of Hafr Al-Batin (UoHB) Hafar Al-Batin KSA Department of Mathematics University of Taif Taif KSA Department of Mathematics University of Kordofan El-Obeid Sudan

In this paper, we shall be concerned with the numerical solution of parabolic equations in one space variable and the time variable t. We expand Taylor series to derive a higher-order approximation for Ut. We begin with the simplest model problem, for heat conduction in a uniform medium. For this model problem, an explicit difference method is very straightforward in use, and the analysis of its error is easily accomplished by the use of a maximum principle. As we shall show, however, the numerical solution becomes unstable unless the time step is severely restricted, so we shall go on to consider other, more elaborate, numerical methods which can avoid such a restriction. The additional complication in the numerical calculation is more than offset by the smaller number of time steps needed. We then extend the methods to problems with more general boundary conditions, then to more general linear parabolic equations. Finally, we shall discuss the more difficult problem of the solution of nonlinear equations.

关键词： Partial Differential Equations (PDEs) homentropic Spatial Derivatives with Finite Differences Central Differences Finite Differences

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